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Prove that the curves x=4 (costheta+sint...

Prove that the curves x=4 `(costheta+sintheta)` and y=3 `(costheta-sintheta)` represents an ellipse.

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`x=4(costheta+sintheta)`
`rArr" "(x)/(4)=costheta+sintheta` . . . (1)
and `y=3(costheta+sintheta)`
`rArr" "(y)/(3)=costheta-sintheta` . . . (2)
Squaring and adding eqs. (1) and (2)
`(x^(2))/(16)+(y^(2))/(9)=(costheta+sintheta)^(2)+(costheta-sintheta)^(2)=2`
`rArr" "9x^(2)+16y^(2)=288`.
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